Strong Field and Nonlinear X-ray Optical Science

Our goal is to understand and control fundamental high-intensity laser-matter interactions. Our particular interests are in ultrafast electronic processes in solids in the mid-infrared and the x-ray wavelength range, where the physics is widely unexplored.

The mid-infrared wavelength range is interesting because of the large ponderomotive energies (Up) and associated tunneling dynamics at high intensity. Here, the applied field can not be thought of as producing a small perturbation to the Hamiltonian therefore the perturbative approach is not appropriate. Thus, we encounter various nonperturbative phenomena playing defining roles in laser solid interaction as seen recently in high-order harmonic generation in crystals.

The x-ray wavelength range has recently become rich because of the high peak power and focusing ability at x-ray free-electrons lasers such as the LCLS. While the applications such as in the nonperiodic imaging of biomolecules are emerging the required fundamental knowledge in the x-ray matter interactions at high-intensity is still yet to flourish. We conduct x-ray nonlinear and quantum optics experiments at the LCLS locally and at the SACLA in Japan.

High-order harmonic generation (HHG) in the strong-field limit has been a standard route to produce attosecond pulses. So far, the interacting medium is a gas. In a recent Nature Physics Letter, we reported the generation of nonperturbative harmonics in a bulk crystal for the first time. Harmonics as high as of 25th orders were produced in a 500 micrometer thick ZnO single crystal when subjected to strong mid-infrared laser pulses of maximum field strength 0.6 V/A. Interestingly, we have found fundamental differences to the atomic HHG for example in the scaling of high-energy cutoff, attributed to the role of periodic potential in crystals. We measured odd only and odd and even harmonics depending upon the orientation of the c-axis of the crystal with respect to the laser polarization as shown in the figure, a strong evidence that the harmonics are not from surface. We explore the possibility of attosecond pulses in high density and crystalline targets for high efficiency.

Redshift in the Optical Absorption of ZnO Single Crystals in the Presence of an Intense Midinfrared Laser Field

Nonperturbative effects are expected in high-intensity laser solid interaction when the ponderomotive energy (Up) exceeds the photon energy and becomes comparable to the band gap of solids. We performed optical absorption measurements in ZnO single crystals in the presence of an intense, (up to 5 TW/cm2) laser at 3.25 micrometer wavelength. In the effective mass approximation, the corresponding Up=35 eV, 10 times larger than the band gap and much larger than the photon energy. This regime of laser solid interaction had never been accessed before.

We observed a substantial redshift (>10% of the band gap) in the absorption edge of crystal at the highest intensity in a pump probe measurement. This effect is of a transient nature as it is present only during the pump probe overlap inside the crystal as shown in the figure. At the moderate laser intensities the redshift scaled to the cube root of the intensity as expected in the Franz-Keldysh scaling but higher intensities showed a new scaling. The change in scaling occurred in the same regime of nonperturbative high-order harmonic generation.

The mechanism for high-order harmonic generation (HHG) in periodic solids is fundamentally different from the atomic HHG as shown by our measurements, for example the different high-energy cutoff scalings. The semiclassical re-scattering approach of HHG fails qualitatively in solids because the typical recursion distances are much larger than the lattice spacing and effects of the periodic potential must be considered.

Nonperturbative harmonics in periodic solids could arise in a two step process comprising tunneling between valance and conduction band, and radiation from the electrons undergoing a frequency modulated Bloch oscillations in the conduction band in presence of a strong field laser.

In this work we calculate the efficiency of harmonics and include the propagation effects which shows that the harmonics should have a temporal profile consisting of a train of pulses with duration on the order of 650 as depending on the crystal thickness as shown in the figure.